from the correct position. With the definitions taken,
a double corner (like on a checker board, figure 3a)
has q = 1; a single ideal corner (figure 3b) has q =
0.75. For intensity distributions allowing good
planar approximations, q goes towards 0. The
threshold value q
min
may be adapted from experience
in the domain. Minimal circularity values for stable
corners should be set around q
min
≈ 0.7. According to
eq. (18) this yields λ
2N
values smaller than about 0.3.
When too many corner candidates are found, it is
possible to reduce their number not by lifting q
min
but by adjusting the threshold value ‘traceN
min
’
which limits the sum of the two eigenvalues.
According to the main diagonal of eq. (15) this
means prescribing a minimal value for the sum of
the squares of all local gradients in the mask. This
parameter depends on the absolute magnitude of the
gradient components and has thus to be adapted to
the actual situation at hand. It is interesting to note
that the threshold ErrMax for planarity check (eq.
13) has a similar effect as the boundary for the
threshold value traceN
min
on corners.
Figure 10 shows corners (black crosses) found
in nonplanarity regions (white bars) in vertical (left)
and horizontal search (right) on the first pyramid
level (m
c
= n
c
= 2 yielding a reduced image of about
45,000 cells). Mask size with m = n = 2 thus was 4·4
= 16 pixel. 2001 nonplanarity features (~ 4.4 % of
number of cells) with interpolation errors larger than
ErrMax = 5 % have been found in vertical search.
From these, 108 locations (dark crosses) have been
determined satisfying the corner conditions:
circularity q
min
= 0.7 and traceN
min
= 0.2 (figure 10,
left). The right-hand part of the figure shows result
of horizontal search with the same parameters except
traceN
min
= 0.15 (reduced for increasing the number
of accepted corners). 865 mask locations (~1.9 %)
yield 40 corner candidates (dark crosses). By
adjusting threshold levels, the number of corner
features obtained can be modified according to the
needs in actual applications. Combining corner
features obtained with different cell- (m
c
, n
c
) and
mel-sizes (m, n) yet has to be investigated; it is
expected that this will contribute to achieving
increased robustness.
The results in row and column search differ
mainly because stripes are shifted by half-stripe
width n (here = 2) laterally, while in search direction
masks are shifted by just one cell.
_____________________________________________________
Acknowledgement: Numerical results are based on software
derived from (Hofmann, 2004)
9 CONCLUSIONS
Checking for the goodness of planarity conditions
when fitting local linear intensity models to image
segments has led to the new ‘nonplanarity’-feature.
In typical road scenes, only 1 to 5 % of all mask
locations exceed threshold values of 3 to 10 %
planarity error (residue values). This yields an
efficient pre-selection for checking corner features.
The gradient components between the mask
elements are used in multiple ways to determine
nonplanar intensity regions, corners, edges and
segments with linear shading models. Merging of
these features over neighboring stripes leads to
larger 2-D features. Some applications to road
scenes have shown the efficiency achievable.
REFERENCES
Birchfield S 1994. KLT: An Implementation of the
Kanade-Lucas-Tomasi Feature Tracker.
http://www.ces.clemson.edu/~stb/klt/
Dickmanns Dirk 1992. KRONOS, Benutzerhandbuch,
1995, UniBwM/LRT
Dickmanns E.D.; Graefe V.: a) Dynamic monocular
machine vision. Machine Vision and Applications,
Springer International, Vol. 1, 1988, pp 223-240. b)
Applications of dynamic monocular machine vision.
(ibid), 1988, pp 241-261
Dickmanns ED, Wuensche HJ 1999. Dynamic Vision for
Perception and Control of Motion. In: B. Jaehne, H.
Haußenecker, P. Geißler (eds.) Handbook of Computer
Vision and Applications, Vol. 3, Academic Press,
1999, pp 569-620
Haralick RM, Shapiro LG 1993. Computer and Robot
Vision. Addison-Wesley, 1992 and 1993.
Harris CG, Stephens M 1988. A combined corner and
edge detector. Proc. 4
th
Alvey Vision Conference, pp.
147-153
Hofmann U 2004. Zur visuellen Umfeldwahrnehmung
autonomer Fahrzeuge. Dissertation, UniBw Munich,
LRT.
Mysliwetz B 1990. Parallelrechner-basierte Bildfolgen-
Interpretation zur autonomen Fahrzeugsteuerung.
Dissertation, UniBw Munich, LRT.
Moravec H 1979. Visual Mapping by a Robot Rover.
Proc. IJCAI 1079, pp 598-600.
Price K , (continuously). http://iris.usc.edu/Vision-
Notes/bibliography/contents.html .
Shi J, Tomasi C 1994. Good Features to Track. Proc.
IEEE-Conf. CVPR, pp. 593-600
Tomasi C, Kanade T 1991. Detection and Tracking of
Point Features. CMU-Tech.Rep. CMU-CS-91-132
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